It was a limited victory at a very high cost.

I think you mean to ask "Did British success at the Battle of the Somme boost morale on the home front?" While it's hard to say for sure, I would guess that it did not. The loss of human life was horrendous, and this was one of Britain's first major battles in the war. Not being used to massive casualties, I'd imagine those back home were as taken aback as they were pleased with the outcome.

I think you mean to ask "Did British success at the Battle of the Somme boost morale on the home front?" While it's hard to say for sure, I would guess that it did not. The loss of human life was horrendous, and this was one of Britain's first major battles in the war. Not being used to massive casualties, I'd imagine those back home were as taken aback as they were pleased with the outcome.